WiFi should not be a problem.
The only thing to watch for is that your phone needs to be GSM not CDMA, and needs to support at least the 900MHz and 1800MHz bands.
The phone's manufacturer should have a website listing compatibility across carriers around the world. Example: here is Apple's page listing iPhone compatibility with LTE bands around the world.
Yes, you use them without any problem.
Some of them want an earthed/grounded plug to reach maximum speed, but without that they still work (though slower).
As for personal experience: I used a pair in a old flat (1950-ish build?) and in my parent house (1975-ish with lots of different power groups and 16 fuses. Basically one fuse per room). No problems ...